You come across an open container which is filled with two liquids. Since the tw

Question

You come across an open container which is filled with two liquids. Since the two liquids have different density there is a distinct separation between them. Water fills the lower portion of the container to a depth of 0.221 m which has a density of 1.00 × 103 kg/m3. The fluid which is floating on top of the water is 0.328 m deep. If the absolute pressure on the bottom of the container is 1.049 × 105 Pa, what is the density of the unknown fluid? The acceleration due to gravity is g = 9.81 m/s2 and atmospheric pressure is P0 = 1.013 × 105 Pa.

Explanation / Answer

density = mass / volume

density = mass / area * depth

density * g = mass * g / area * depth

density * g = gravitational force / area * depth

gravitational force / area = pressure

density * g = pressure / depth

pressure = density * g * depth

pressure = 1.049 * 10^5 - 1.013 * 10^5

pressure = 0.036 * 10^5 Pa

0.036 * 10^5 = density_water * g * depth_water + density_liquid * g * depth_liquid

0.036 * 10^5 = 1000 * 9.8 * 0.221 + density_liquid * 9.8 * 0.328

density of liquid = 446.17969 kg/m^3

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